hip roof garage & sloping shed

What's the best way to join a tiled hip roof garage and a sloping sheet metal shed. The shed is positioned at the back of the garage on the shorter wall. The back wall of the garage is the common wall. Thus the guttering of the garage is visible inside the shed. I've added a rough sketch. The problem area is the garage guttering between the garage and the shed. I was thinking of putting a new sheet metal roof on the shed and connecting to the rear tiled hip roof of the garage with a more gentle slope to the back rather than the side. However, this would affect the width and height of the shed. I was wondering what are my options? I'd prefer not to completely demolish the shed.

I'd say get a roofer's sheet metal shop to make up a box gutter and a tapered flashing, either to replace your gutter on the garage, or to slip behind it.
See the attachment.
Regards
Bill

Thanks Bill for the sketch. Your site is good read. Roofing is a whole new world to me. many thanks Wes